In previous works [1]}, [2]}, a detailed study of the feasibility of small topological trapped-ion QEC codes under realistic models of noise has been presented. These studies focused on mixed-species ion crystals in micro-fabricated traps, exploiting shuttling and ion crystal reconfigurations for the implementation of QEC protocols. With the advent of improved laser focusing techniques for both single and two-qubit gates, it is nowadays possible to realize these small QEC codes in a static string approach. Note, however, that the absence of shuttling requires a careful reconsideration of the error model: the close proximity of spectator ions in the string during gates addressed at active ions requires a careful consideration of crosstalk noise, which was not considered previously [1]}, [2]}.
As shown by the results of our numerical simulations, bare crosstalk can compromise the demonstration of quantum logic advantage, as it places the regime of beneficial QEC within very small values of the crosstalk error rates, which are out of the scope of current experimental technologies.
As discussed in our work, the coherent nature of this noise allows us to design a refocusing scheme to actively suppress crosstalk, ultimately placing the pseudo-thresholds of quantum logic advantage within reach of near-term trapped-ion experiments. In this way, one can benefit from the simplicity of the static-string approach, and achieve quantum logic advantage in analogy to the shuttling-based approach [1]}, [2]}.
